How do I find and get to the Greybeards?

I was doing the quest where you have to find and speak to the Greybears about your new shout ability. The quest marker led me to Ivanstead and it took me a good twenty or thirty minutes to run there. When I got there the quest marker was gone, and on a new place on top of a mountain. I fast traveled to the nearest location but to my suprise, I could not find a way up the steep snowy mountain.

Why did it change? Where are the greybeards exactly? And I do I get to them?

Top Voted Answer

Go to Ivarsteed. At the bridge there will be two guys talking about the 7000 step hike to High Hrothgar. Accept to take the donations to the gray beards, follow the road up to the mountain. Climb the stairs all the way to the top. At the bottom of the steps at the entrance of High Hrothgar will be a chest, place the donations into the chest and go up the stairs and enter the temple.

There are 7000 steps originally, but years of tear and wear has destroyed most of them plus some of them are covered in snow.